Constant RMR Solutions to Reader Writer Synchronization

We study Reader-Writer Exclusion, a well-known variant of the Mutual Exclusion problem where processes are divided into two classes--readers and writers--and multiple readers can be in the Critical Section (CS) at the same time, although no process may be in the CS at the same time as a writer. Since readers don\u27t conflict with each other, they should not obstruct each other. Specifically, the concurrent entering property must be satisfied: if all writers are in the remainder section, each reader should be able to enter the CS in a bounded number of its own steps. Three versions of the Reader-Writer Exclusion problem are commonly studied--one where writers have priority over readers, another where readers have priority, and the last where neither class has priority over the other and no process may starve. To ensure high performance on Cache-Coherent (CC) and Distributed Shared Memory (DSM) multiprocessors, algorithms should be designed to generate as few remote memory references (RMRs) as possible. The ideal would be to achieve constant RMR complexity, i.e., the worst case number of RMRs that a process generates in order to enter and exit the CS once is a constant, independent of the number of processes. Constant RMR complexity algorithms have existed for Mutual Exclusion for two decades, but none exists for Reader-Writer Exclusion. Danek and Hadzilacos\u27 lower bound proof implies that it is impossible to achieve sublinear RMR complexity for DSM machines. For CC machines, the best existing bound, also due to Danek and Hadzilacos , is O(log n), where n is the number of processes. In this work, we present the first constant RMR complexity algorithms for all three versions of the Reader-Writer Exclusion problem (for CC machines)

The Weakest Failure Detector to Solve Mutual Exclusion

Mutual exclusion is not solvable in an asynchronous message-passing system where processes are subject to crash failures. Delporte-Gallet et. al. determined the weakest failure detector to solve this problem when a majority of processes are correct. Here we identify the weakest failure detector to solve mutual exclusion in any environment, i.e., regardless of the number of faulty processes. We also show a relation between mutual exclusion and consensus, arguably the two most fundamental problems in distributed computing. Specifically, we show that a failure detector that solves mutual exclusion is sufficient to solve non-uniform consensus but not necessarily uniform consensus

ANALYSIS ON IMPLEMENTATION AND ITS FURTHER IMPROVEMENTS OF AKS CLASS ALGORITHMS

The present work has been carried out at CSIR Centre for Mathematical Modeling and Computer Simulation (C-MMACS). The paper deals with the implementation of AKS class primality tests and various issues relating to it. AKS algorithm is the first deterministic polynomial time primality test named after its authors Manindra Agarwal, Neeraj Kayal and Ntin Saxena. A primality-testing algorithm is one that checks whether a given number is prime or not. “Deterministic ” means that operations carried out by the algorithm are determined entirely by (1) the algorithm (2) the input. In particular the algorithm does not make any 1 random choices. “Polynomial time ” means that there is some polynomial p such that, for every input n, the algorithm takes at most p (length of n) steps. This algorithm is presented in the paper “ Primes in P ” [4] and since then many efforts are being made to implement the same. In this paper we have implemented the AKS algorithm and have provided the complexity at each step of the algorithm. We hav

Tight Time-Space Tradeoff for Mutual Exclusion

Mutual Exclusion is a fundamental problem in distributed computing. Proving upper and lower bounds on the RMR complexity of this problem and its variants has been a topic of intense research in the last two decades. We add a novel dimension to this research by proving matching lower and upper bounds on how RMR complexity trades off with space. Two exciting implications of our results are that constant RMR complexity is impossible with subpolynomial space and subpolynomial RMR complexity is impossible with constant space (for cache-coherent multiprocessors, regardless of how strong the hardware synchronization operations are). We believe that our technical contributions are equally exciting. A highlight is that, even though mutual exclusion is a “messy ” problem to analyze because of system details such as asynchrony and cache coherence, we show that a simple and purely combinatorial bin-pebble game that we design exactly captures the complexity of the mutual exclusion problem. Lower bound proofs in distributed computing are typically based on covering, bivalency, or other indistinguishability arguments. In contrast, our lower bounds are based on the potential method, and we believe this is the first use of this method in lower bounds for distributed computing

Vagus nerve stimulation paired with rehabilitation for stroke: Implantation experience from the VNS-REHAB trial.

Objective: Vagus Nerve Stimulation (VNS) paired with rehabilitation delivered by the Vivistim® Paired VNS™ System was approved by the FDA in 2021 to improve motor deficits in chronic ischemic stroke survivors with moderate to severe arm and hand impairment. Vagus nerve stimulators have previously been implanted in over 125,000 patients for treatment-resistant epilepsy and the surgical procedure is generally well-tolerated and safe. In this report, we describe the Vivistim implantation procedure, perioperative management, and complications for chronic stroke survivors enrolled in the pivotal trial. Methods: The pivotal, multisite, randomized, triple-blind, sham-controlled trial (VNS-REHAB) enrolled 108 participants. All participants were implanted with the VNS device in an outpatient procedure. Thrombolytic agents were temporarily discontinued during the perioperative period. Participants were discharged within 48 hrs and started rehabilitation therapy approximately 10 days after the Procedure. Results: The rate of surgery-related adverse events was lower than previously reported for VNS implantation for epilepsy and depression. One participant had vocal cord paresis that eventually resolved. There were no serious adverse events related to device stimulation. Over 90% of participants were taking antiplatelet drugs (APD) or anticoagulants and no adverse events or serious adverse events were reported as a result of withholding these medications during the perioperative period. Conclusions: This study is the largest, randomized, controlled trial in which a VNS device was implanted in chronic stroke survivors. Results support the use of the Vivistim System in chronic stroke survivors, with a safety profile similar to VNS implantations for epilepsy and depression